Conservatives are likely to try blame the knock-on effects of the crisis in the euro area for sluggish growth at home

Margaret Thatcher had Jacques Delors and Tony Blair had Jacques Chirac. Will David Cameron’s bête noire in the European Union be yet another Frenchman?

Certainly the mood music before the first summit handshake between the prime minister and the new socialist French president, François Hollande, has been far from harmonious. Cameron “snubbed” Hollande when he visisted London recently – despite the fact that Hollande looked odds-on to win the presidency. Hollande, in turn, has done little to disguise his disdain for British attitudes to Europe, as espoused by the likes of Cameron.

Last week the new president criticised what he said was the British “obsession” with protecting the City of London from EU legislation, as he pushed his own plans for more fiscal harmonisation. “And to that,” Hollande said, “is added a relative indifference to the fate of the eurozone.” The Brits, he suggested, took from Europe but gave little back. “Europe is not a cash till and less still a self-service restaurant,” was the image he chose.

While Paris and Berlin will have their work cut out keeping the Franco-German motor in order over the coming days and weeks – with Hollande arguing for an easing of austerity and Merkel determined to stick to it – the immediate future of the Anglo-French entente is in question too.

Hollande could hardly be further away from Cameron, ideologically, economically and in his broad attitudes to Europe. While austerity defines Cameron’s premiership at home, moves to loosen it defined the new president’s successful campaign for the Elysée and are at the centre of his short-term plans for the EU. Hollande has said he wants to reopen the EU’s nascent “fiscal treaty” so that austerity can be balanced with stronger commitments to restoring growth. He also wants a tax on financial services – which the UK refuses even to consider.

Hollande’s solutions to the EU crisis are for Europe to do more, spend more, regulate more, while Cameron’s are for it to do less, spend less and deregulate. Hollande believes in Europe, a social Europe, Cameron does not.

The gulf between this Tory prime minister and socialist president, who will be sworn in on Tuesday, is already wide. But it could get wider – not least because of the dire problems Cameron has suddenly found himself facing on the domestic front.

With the UK economy now back in recession, and showing few signs of a speedy emergence from it, the coalition parties (particularly the Tories) are likely to try blame the knock-on effects of the crisis in the euro area for sluggish growth. Cameron stated the obvious when he said the euro was in “extreme difficulty” – but he implied as he did so that everyone would feel the chill, including countries like his that lie outside the single currency.

There is little that will infuriate the French and Germans more than the UK blaming its own problems on the EU, in which it has always refused to participate as fully as the true believers in Paris and Berlin.

But this is just one reason to doubt whether Cameron can ever have warm relations with Hollande. Cameron, bruised by his party’s recent drubbing in local elections, is under pressure from the right of his party. And that means pressure to show more anti-EU mettle. The prime minister will know full well that the moment he was most popular in his own party was after he vetoed a new treaty, or fiscal pact, last December. Cameron insisted on securing concessions on, and exemptions from, EU financial-markets regulation as the price of his assent to a German-led plan to save the euro. He did not get them, so he blocked a full EU deal. Tories were thrilled by his defiance.

Many in his own party now believe he can revive his and the Tories’ fortunes if he shows such resolve again. One opportunity to do so will be during negotiations of the new EU budget, which begin in earnest later this year. Cameron is under pressure to drive a hard deal, heading off what is likely to be pressure from the other 26 nations to end the British rebate. Ministers say he might conclude that the best way of entering an election campaign in 2015 will be off the back of a budget battle with the EU as big and successful as that waged by Thatcher in 1984 at Fontainebleau when she secured the rebate in the first place.

Earlier this year a tacit agreement is rumoured to have been made between Cameron and Hollande’s predecessor, Nicolas Sarkozy, that the French would not insist too strongly that the UK gives up its £2bn-a-year rebate if the British agreed not to demand too much reform of the common agricultural policy which benefits France’s tens of thousands of small farmers. The word is that Hollande is unlikely to want to renew such a deal and will go flat out to end the rebate. The UK could then target the CAP. EU diplomats foresee an ugly battle.

Cameron will also be under huge pressure from his backbenchers to place a commitment to some form of referendum on Britain’s relations with the EU in the next Tory election manifesto. Ministers insist that no such discussions have taken place in government or in the Tory party about this. But there is an acceptance that Cameron will be unable to keep order among his troops – already frustrated by coalition with the Lib Dems – without the “red meat” of a big-order election pledge on Europe.

The Tories are aware that the last time they ran a hardline Eurosceptic election campaign, under William Hague in 1997, it was a disastrous failure. But that, they say, was when the euro was in its planning stage and much of Europe was queueing up to join. Now it is at risk of falling apart, many are convinced such an approach can work. What then for the entente?